Finite Group Databasebeta

← #14271676

Subgroups — #14271676

Order 1856.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90809C211yesmaximal, characteristic, complemented
2C22×C4×D29C211yesmaximal, characteristic, complemented
3C29×C22⋊Q8C211yesmaximal, characteristic, complemented
4#11745308C211yesmaximal, characteristic, complemented
5#11745292C211yesmaximal, characteristic, complemented
6#11745257C211yesmaximal, characteristic, complemented
7#11745256C212yesmaximal, complemented
8#11745255C212yesmaximal, complemented
9#11745254C211yesmaximal, characteristic, complemented
10#11745244C212yesmaximal, complemented
11#11745243C212yesmaximal, complemented
12C23×D29C2211yescharacteristic
13C2×Q8×C29C2211yescharacteristic, complemented
14C22×C4×C29C2211yescharacteristic
15C2×C22⋊D29C2212yes—
16C22×Dic29C2211yescharacteristic
17#90809—24no—
18C2×D116C2212yes—
19C2×D116C2212yes—
20C2×D116C2211yescharacteristic, complemented
21C2×C4×D29—24no—
22C2×C4×D29C2211yescharacteristic
23C2×C4×D29C2211yescharacteristic
24C2×C4×D29C2211yescharacteristic
25C2×C4×D29C2211yescharacteristic
26C2×C4×D29C2212yescomplemented
27C4⋊C4×C29C2211yescharacteristic, complemented
28C4⋊C4×C29C2212yescomplemented
29C22⋊C4×C29C2212yes—
30#90781C2212yes—
31#90781C2212yes—
32#90781C2212yescomplemented
33#90781C2212yescomplemented
34C4⋊Dic29C2211yescharacteristic, complemented
35#90779C2212yescomplemented
36C4×Dic29C2212yescomplemented
37C23×C29C2311yescharacteristic
38C22×D29—22no—
39C22×D29—22no—
40C22×D29—22no—
41C22×D29C2312yes—
42C22×D29C2311yescharacteristic
43C22×D29C2311yescharacteristic
44Q8×C29—22no—
45C2×C4×C29—22no—
46C2×C4×C29C2312yes—
47C2×C4×C29C2312yes—
48C2×C4×C29C2311yescharacteristic
49C2×C4×C29C2311yescharacteristic
50C22⋊D29—24no—
51C2×Dic29—22no—
52C2×Dic29C2312yes—
53C2×Dic29C2311yescharacteristic
54C2×Dic29C2311yescharacteristic
55D116—24no—
56D116—24no—
57D116—22no—
58C4×D29—22no—
59C4×D29—22no—
60C4×D29—22no—
61C4×D29—24no—
62C4×D29D414yescomplemented
63C22×C29—21no—
64C22×C29—21no—
65C22×C29#4112yescomplemented
66C22×C29C2411yescharacteristic
67C2×D29—28no—
68C2×D29—21no—
69C2×D29—21no—
70C2×D29—21no—
71C2×D29—21no—
72C2×D29—22no—
73C2×D29—22no—
74C2×D29—22no—
75C2×D29C2×D412yes—
76C2×D29#4112yescomplemented
77C4×C29—21no—
78C4×C29—22no—
79C4×C29—22no—
80C4×C29C2×D412yes—
81Dic29—21no—
82Dic29—22no—
83Dic29C2×D412yes—
84#525—291nomaximal, Sylow
85C2×C29—22no—
86C2×C29C22×D411yescharacteristic
87C2×C29C2×#4111yescharacteristic
88C2×C29C2×#4111yescharacteristic
89D29—22no—
90D29—22no—
91D29—42no—
92C2×#41—291no—
93C23×C4—291no—
94#123—292no—
95C22⋊Q8—291no—
96C22⋊Q8D2911yescharacteristic, complemented
97#121—291no—
98#121—291no—
99#120—292no—
100C4×D4—292no—
101C4×D4—292no—
102#117—291no—
103C29#52511yescharacteristic, complemented, Sylow
104C24—291no—
105#41—584no—
106C2×Q8C2×D2911yescharacteristic, complemented
107C2×D4—292no—
108C2×D4—292no—
109C2×D4—292no—
110C2×D4—291no—
111C22×C4—291no—
112C22×C4—291no—
113C22×C4—291no—
114C22×C4—292no—
115C22×C4—291no—
116C22×C4—291no—
117C22×C4—584no—
118C22×C4C2×D2911yescharacteristic
119C4⋊C4—291no—
120C4⋊C4—292no—
121C4⋊C4C2×D2911yescharacteristic, complemented
122C4⋊C4C2×D2912yescomplemented
123C22⋊C4—292no—
124C22⋊C4—292no—
125C22⋊C4—292no—
126C22⋊C4—292no—
127C22⋊C4C2×D2912yes—
128C42—292no—
129C23—291no—
130C23—291no—
131C23—292no—
132C23—582no—
133C23—582no—
134C23—582no—
135C23C22×D2911yescharacteristic
136Q8—22no—
137D4—584no—
138D4—584no—
139D4—584no—
140D4—582no—
141C2×C4—22no—
142C2×C4—291no—
143C2×C4—294no—
144C2×C4—292no—
145C2×C4—291no—
146C2×C4—582no—
147C2×C4—584no—
148C2×C4—582no—
149C2×C4—582no—
150C2×C4—582no—
151C2×C4C22×D2912yes—
152C2×C4C22×D2911yescharacteristic
153C2×C4C22×D2912yes—
154C2×C4C22×D2911yescharacteristic
155C22—21no—
156C22—21no—
157C22—292no—
158C22—292no—
159C22—588no—
160C22—581no—
161C22—581no—
162C22—581no—
163C22—581no—
164C22—582no—
165C22—582no—
166C22—582no—
167C22#9080912yescomplemented
168C22C23×D2911yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—292no—
173C4—581no—
174C4—582no—
175C4D4×D2912yes—
176C2—22no—
177C2—582no—
178C2—582no—
179C2—1162no—
180C2C2×D4×D2911yescharacteristic
181C2C2×#9080911yescharacteristic
182C2#41×D2911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×C22⋊Q8C2
hypercenterC22⋊Q8D29
hypocenterC29#525
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#90809C2semidirect
2. C22×C4×D29C2semidirect
3. C29×C22⋊Q8C2semidirect
4. #11745308C2semidirect
5. #11745292C2semidirect
6. #11745257C2semidirect
7. #11745256C2semidirect
8. #11745255C2semidirect
9. #11745254C2semidirect
10. #11745244C2semidirect
11. #11745243C2semidirect
13. C2×Q8×C29C22semidirect
20. C2×D116C22semidirect
26. C2×C4×D29C22semidirect
27. C4⋊C4×C29C22semidirect
28. C4⋊C4×C29C22semidirect
32. #90781C22semidirect
33. #90781C22semidirect
34. C4⋊Dic29C22semidirect
35. #90779C22semidirect
36. C4×Dic29C22semidirect
62. C4×D29D4semidirect
65. C22×C29#41semidirect
76. C2×D29#41semidirect
96. C22⋊Q8D29semidirect
103. C29#525semidirect
106. C2×Q8C2×D29semidirect
121. C4⋊C4C2×D29semidirect
122. C4⋊C4C2×D29semidirect
167. C22#90809semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#908092
C22×C4×D292
C29×C22⋊Q82
#117453082
#117452922
#117452572
#117452562
#117452552
#117452542
#117452442
#117452432
#52529